-- Exercise 1

data Rat = Rat Integer Integer

normaliseRat :: Rat -> Rat
normaliseRat = undefined

createRat :: Integer -> Integer -> Rat
createRat = undefined

instance Eq Rat where
-- to implement

instance Ord Rat where
-- to implement

instance Show Rat where
  show r = undefined

instance Num Rat where
-- to implement

-- Exercise 2

data Vegetable -- to be defined

data Candy -- to be defined

type Shoppinglist a = [(a,Integer)] -- item and quantity

veggies :: Shoppinglist Vegetable
veggies = undefined -- [ (Corn Store, 2), (Corn Named, 3), (Mushroom Named, 1), (Beans, 5) ]

candies :: Shoppinglist Candy
candies = undefined -- [ (Duplo Family, 1), (Twix Single, 5), (Balisto, 2) ]

class Cost a where
-- to implement

instance Cost Candy where
-- to implement

instance Cost Vegetable where
-- to implement

shoppingCosts :: Cost a => Shoppinglist a -> Double
shoppingCosts = undefined

-- Tests
{-
the tests currently do not compile because of the
non-availibility of the data types of exercise 2;
activate the tests after their definitions by removing
the comment delimiters {- .. -} around tests.
-}

{- 
tests = do
  --Rational Number tests
  check "normaliseRat" "True" (case (normaliseRat (Rat (-1) (-2)), normaliseRat (Rat 2 4)) of
    (Rat n1 d1, Rat n2 d2) -> (n1, d1) == (n2, d2))
  check "createRat" "-1/2" (createRat 5 (-10))
  check "Equality on Rats" "[True,False]" ([Rat 3 5 == Rat (-9) (-15), Rat 3 5 == Rat 5 3])
  check "Order on Rats" "[True,False,True]"
    ([Rat 3 5 < Rat 3 4, Rat 2 4 < Rat 2 4, Rat (-5) 3 < Rat 10 1])
  check "Show on Rats" "[3,4/5,-1/2]" ([Rat 3 1, Rat 4 5, Rat 1 (-2)])
  check "Num on Rats" "[1/2,7/12,3/4,-1]"
    ([3 * Rat 1 6, Rat 1 3 + Rat 1 4, abs (Rat (-3) 4), signum (negate (Rat 3 4))])
  --Typeclass tests
  let veggiesTest = [(Mushroom Store, 20), (Beans, 101), (Corn Named, 1)]
  let candiesTest = [(Twix Medium, 2), (Duplo Single, 10), (Duplo Single, 100)]
  check "Cost function" "[0.5,3.49,2.39,2.59,1.79,0.89]"
    ([cost (Duplo Single), cost (Duplo Family), cost (Twix Medium),
    cost (Corn Named), cost (Mushroom Store), cost Beans])
  check "shoppingCosts function" "[17.15,8.99,128.28,59.78]"
    ([shoppingCosts veggies, shoppingCosts candies,
    shoppingCosts veggiesTest, shoppingCosts candiesTest])
-}

check name e c = do
  putStr ("*** " ++ name ++ ": ")
  if show c == e then putStrLn "OK"
  else putStrLn ("ERROR; expected '" ++ e ++ "', but found '" ++ show c ++ "'")